Search for Majorana Fermions in Superconductors

2011/12/31 by C. W. J. Beenakker, C.W.J. Beenakker · 1,839 citations
Materials Science · Physics and Astronomy · #Bound state #Chemical and Physical Properties of Materials #Coherence (philosophical gambling strategy) #Fermion #MAJORANA #Majorana equation #Majorana fermion #Qubit #Rare-earth and actinide compounds #Superconductivity #Topological Materials and Phenomena #cond-mat.mes-hall

paper · pdf · open access · doi:10.1146/annurev-conmatphys-030212-184337

published in Annual Review of Condensed Matter Physics 4(1), 113-136 (Annual Reviews) · 15 pages; 13 figures; version 2: experimental update

arxiv created 2012/04/12 · openalex publication_date 2013/03/08 · arxiv updated 2013/03/12 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

Majorana fermions (particles that are their own antiparticle) may or may not exist in nature as elementary building blocks, but in condensed matter they can be constructed out of electron and hole excitations. What is needed is a superconductor to hide the charge difference and a topological (Berry) phase to eliminate the energy difference from zero-point motion. A pair of widely separated Majorana fermions, bound to magnetic or electrostatic defects, has non-Abelian exchange statistics. A qubit encoded in this Majorana pair is expected to have an unusually long coherence time. I discuss strategies to detect Majorana fermions in a topological superconductor, as well as possible applications in a quantum computer. The status of the experimental search is reviewed.

Citations

• Charge insensitive qubit design derived from the Cooper pair box
• Signatures of Majorana fermions in hybrid superconductor-semiconductor nanowire devices
• Detecting Majorana bound states
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• Topological Insulators
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• Chain of Majorana States from Superconducting Dirac Fermions at a Magnetic Domain Wall
• Fault-tolerant quantum computation by anyons
• Observing Majorana bound States inp-Wave Superconductors Using Noise Measurements in Tunneling Experiments
• Non-Abelian anyons and topological quantum computation
• Nonabelions in the fractional quantum hall effect
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Cited by

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• Doubled Shapiro steps in a topological Josephson junction
• Weyl nodes in periodic structures of superconductors and spin-active materials
• Andreev bound states versus Majorana bound states in quantum dot-nanowire-superconductor hybrid structures: Trivial versus topological zero-bias conductance peaks
• Quantized zero-bias conductance plateau in semiconductor-superconductor heterostructures without topological Majorana zero modes
• Topologically nontrivial Andreev bound states
• Pinning of Andreev bound states to zero energy in two-dimensional superconductor- semiconductor Rashba heterostructures
• Thermoelectric transport through a Majorana zero modes interferometer
• Braiding properties of Majorana Kramers pairs
• Theory of twist liquids: Gauging an anyonic symmetry
• Weak localization and spin-orbit interaction in side-gate field effect devices at theLaAlO3/SrTiO3interface
• Effective field theories for superconducting systems with multiple Fermi surfaces
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• Interlayer current near the edge of an InAs/GaSb double quantum well in proximity with a superconductor
• Superconducting proximity in three-dimensional Dirac materials: Odd-frequency, pseudoscalar, pseudovector, and tensor-valued superconducting orders
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• A Practical Phase Gate for Producing Bell Violations in Majorana Wires
• Strong Localization of Majorana End States in Chains of Magnetic Adatoms
• Numerical study of PbTe-Pb hybrid nanowires for engineering Majorana zero modes
• Many-terminal Majorana island: From topological to multichannel Kondo model
• Vectorial Control of the Spin–Orbit Interaction in Suspended InAs Nanowires
• Topological Superconductivity in a Planar Josephson Junction
• Majorana-Hubbard model on the square lattice
• Controllable photonic and phononic edge localization via optomechanically induced Kitaev phase
• Prethermal Strong Zero Modes and Topological Qubits
• Topological order in the Kitaev/Majorana chain in the presence of disorder and interactions
• Electrically tunable chiral Majorana edge modes in quantum anomalous Hall insulator–topological superconductor systems
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• Robust Transport Signatures of Topological Superconductivity in Topological Insulator Nanowires
• Evolution of Density of States and a Spin-Resolved Checkerboard-Type Pattern Associated with the Majorana Bound State
• The quest and hope of Majorana zero modes in topological superconductor for fault-tolerant quantum computing: An introductory overview
• Phase-tunable second-order topological superconductor
• Absence of supercurrent sign reversal in a topological junction with a quantum dot
• Fractional Josephson Vortices and Braiding of Majorana Zero Modes in Planar Superconductor-Semiconductor Heterostructures
• Weyl points in systems of multiple semiconductor-superconductor quantum dots
• Conductance smearing and anisotropic suppression of induced superconductivity in a Majorana nanowire
• Unconventional proximity-induced superconductivity in bilayer systems
• Thermally induced metallic phase in a gapped quantum spin liquid: Monte Carlo study of the Kitaev model with parity projection
• Inducing a many-body topological state of matter through Coulomb-engineered local interactions
• Topological Superconductor to Anderson Localization Transition in One-Dimensional Incommensurate Lattices
• Second-Order Topological Superconductors with Mixed Pairing
• Nonlocality and dynamic response of Majorana states in fermionic superfluids
• Magnetic order on a topological insulator surface with warping and proximity-induced superconductivity
• Teleportation-based quantum information processing with Majorana zero modes
• Majorana modes and p-wave superfluids for fermionic atoms in optical lattices
• Dispersive Readout of Majorana Qubits
• Proposal for Measuring the Parity Anomaly in a Topological Superconductor Ring
• Chemistry of Quantum Spin Liquids
• Majorana Edge States in Atomic Wires Coupled by Pair Hopping
• Majorana modes in emergent-wire phases of helical and cycloidal magnet-superconductor hybrids
• Fidelity and visibility loss in Majorana qubits by entanglement with environmental modes
• Quantum gates for Majoranas zero modes in topological superconductors in one-dimensional geometry
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• Superconducting topological surface states in the noncentrosymmetric bulk superconductor PbTaSe 2
• Planar Josephson Hall effect in topological Josephson junctions
• Geometric Induction in Chiral Superconductors
• Quantum anomalous Hall Majorana platform
• Equivalence of topological insulators and superconductors
• Double-dot interferometer for quantum measurement of Majorana qubits and stabilizers*
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• Nearly ferromagnetic spin-triplet superconductivity
• Squeezing light with Majorana fermions
• Dyonic zero-energy modes
• Effect of a tunnel barrier on the scattering from a Majorana bound state in an Andreev billiard
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• Majorana Fermions and Topology in Superconductors
• Topological phases of a dimerized Fermi–Hubbard model for semiconductor nano-lattices
• Sachdev-Ye-Kitaev circuits for braiding and charging Majorana zero modes
• Proposed platform to study interaction-enabled topological phases with fermionic particles
• Topological superconductivity in quantum Hall–superconductor hybrid systems
• Transport signatures of topological superconductivity in a proximity-coupled nanowire
• Tunneling spectroscopy of Majorana-Kondo devices
• Fragility of the Fractional Josephson Effect in Time-Reversal-Invariant Topological Superconductors
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• Fingerprints of Majorana Bound States in Aharonov-Bohm Geometry
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• Tri-component-pairing chiral superconductivity on the honeycomb lattice with mixed s- and d-wave symmetries
• 4π-periodic Josephson supercurrent in HgTe-based topological Josephson junctions
• Localization and Topology in Noncentrosymmetric Superconductors with Disorder
• Holonomic implementation of CNOT gate on topological Majorana qubits
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• Quantum Electronic Transport of Topological Surface States in β-Ag2Se Nanowire

Related

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• Introduction to topological superconductivity and Majorana fermions
• Majorana Fermions: The race continues
• Introduction to Topological Superconductivity and Majorana Fermions for Quantum Engineers
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